# Option Pricing and Volatility Modeling with Python: Implementing Black-Scholes and GARCH Models

Option Pricing is a common problem in Finance that requires pricing financial options. Volatility Modeling is another important concept that focuses on predicting the magnitude of price changes in the stock market. Python is a powerful tool that can be used to model these concepts.

In this tutorial, we will explore how to implement two popular models for Option Pricing and Volatility Modeling in Python: the Black-Scholes Model and the GARCH Model. You will learn how to apply the Black-Scholes model to value European call and put options. The GARCH Model will be used to estimate volatility for stock prices.

To follow along with this tutorial, you should have a basic understanding of Python and finance concepts.

To implement the Black-Scholes Model in Python, we need to import the necessary libraries. We will be using the `numpy` library for mathematical operations and the `matplotlib` library for creating plots.
`import numpy as npimport matplotlib.pyplot as plt`
`def black_scholes_call(S, K, T, r, sigma):    d1 = (np.log(S/K) + (r + sigma**2 / 2) * T) / (sigma * np.sqrt(T))    d2 = d1 - sigma * np.sqrt(T)    C = S * norm.cdf(d1) - K * np.exp(-r * T) * norm.cdf(d2)    return Cdef black_scholes_put(S, K, T, r, sigma):        d1 = (np.log(S / K) + (r + sigma ** 2 / 2) * T) / (sigma * np.sqrt(T))    d2 = d1 - (sigma * np.sqrt(T))    P = K * np.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)    return P`